Now you know how to solve Systems of Linear Equations.  Lets try a word problem that can be solved any way.  In this word problem we will solve it the Linear Combination method.

Example:

A caterer is planning a party for 64 people.  The customer has $150 to spend.  A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people.  How many pans of pasta and how many sandwich trays should the caterer make?

First set up equation 1:

People per pan of pasta= 14
Pans of pasta= X
People per sandwich tray= 6
Sandwich tray= Y
People at party= 64

So now you put this into variable form:
14x+6y=64 is your first equation

Second set up equation 2:

Price per pan of pasta= 39
Pans of pasta= X
Price per sandwich tray= 12
Sandwich trays= Y
Money to spend on food= $150

So now set up the second equation:
39x+12y= 150

Put the together so you can see what method is good to use:

14x+6y= 64
39x+12y=1 50

Now you will divide the first equation by -2 so it would equal:

-28x-12y= -128
39x+12y= 150

Since your Y's will cancel you can solve for X:

X= 2

Now you will take 2 and plug it into one of the orginial equation to find Y:

Y= 6

So your final answer would be (2,6) or you could also say that you can have 2 pans of pasta and 6 sandwich trays for the party.